Determine if the following converges or diverges

Determine if the following converges or diverges as x approaches infinity by either evalutation, the direct comparison test, or the limit comparison test: (It's a Calculus II, AP Calculus BC level of problem)

the integral of (lnx/(square root of (x^2-1))), from 1 to infinity.

* I do not know how to evaluate the integral analytically, so I tried to use either the direct comparison test or limit comparison test. I can't seem to find another function that will "sandwich" that function (and thus prove convergency) or one that will prove it's divergency. I've tried 1/x, 1/(x^2), etc and I'm stuck. Any help on a function to use would be very much appreciated- I'm frustrated beyond belief!

Direct Comparison Test:
0< f(x)< g(x) proves that f(x) converges if g(x) also converges
f(x)> g(x)---proves that f(x) diverges if g(x) diverges
Limit Comparison Test:
if the limit as x approaches infinity of f(x)/g(x) is a finite, non-zero number, then f(x) has the same behavior of convergence as g(x)

look at ln(x)/Sqrt(x^2-1) its only improper at infinity so if you look at what the function looks like when x --> infinity we get ln(x) /x . From this we can compare it to anything that diverges and is smaller than that...easiest example 1/x. ln(x)/Sqrt(x^2-1) > 1/x for all x > 1

thank you, but don't you have to choose a function that is greater/less than for all numbers from 1 to infinity? I don't understand how you can say for x>1, because one itself is the lower limit of the integral and shouldn't it thus be included? or in this type of problem is it to be assumed that the f(x)> g(x) for x>1, not including one?

Fact "a" is inconvenient because it seemingly precludes a direct comparison with 1/x (our hope for a divergence result). So here is the involved part. Below, I will use the expressions "F diverges" and "F = [itex]\infty[/itex]" interchangeably.

there are numerous number of solution to these kind of problems. you asked to show whether it diverges or converges...it diverges if it is larger than something than diverges then it too diverges (remember the converse is not true) 1/(100x) could be an answer that can work all the times but so can 1/(1004x)